Q11 of 319 Page 23

What are the points on y-axis whose distance from the line is 4 units?

Given:

Distance from the line is 4.

To find:

Points on y-axis

Concept Used:

Distance of a point from a line.

Explanation:

Let (0, t) be a point on the y-axis.

It is given that the perpendicular distance of the line from the point (0, t) is 4 units.

∴

⇒

⇒ t

Hence, the required points on the y-axis are and .

Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line.

Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x – 3y = 7.

In the triangle ABC with vertices A(2, 3), B(4, -1) and C(1, 2) find the equation and the length of the altitude from the vertex A.

Show that the path of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line.